2020/07/29 by Duong Thi Viet An, An, Duong Thi Viet, Nguyen Dong Yen +1
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Advanced Banach Space Theory
paper · pdf · doi:10.48550/arxiv.2007.14593
This paper focuses on second-order necessary optimality conditions for\nconstrained optimization problems on Banach spaces. For problems in the\nclassical setting, where the objective function is C2-smooth, we show that\nstrengthened second-order necessary optimality conditions are valid if the\nconstraint set is generalized polyhedral convex. For problems in a new setting,\nwhere the objective function is just assumed to be C1-smooth and the\nconstraint set is generalized polyhedral convex, we establish sharp\nsecond-order necessary optimality conditions based on the Fr 'echet\nsecond-order subdifferential of the objective function and the second-order\ntangent set to the constraint set. Three examples are given to show that the\nused hypotheses are essential for the new theorems. Our second-order necessary\noptimality conditions refine and extend several existing results.\n